The lines y = 2x, 2x + y - 12 = 0 and y = 2 enclose a triangular region of the xy-plane.

Find

a) the coordinates of the vertices of this region

the coordinates of the vertices of this region are : A (3; 6) B (1; 2) C (5; 2)

Step-by-step explanation:

look this solution and graph

see explanation

Step-by-step explanation:

Equate pairs of the equations and solve, that is

y = 2x and y = 2, hence

2 = 2x (divide both sides by 2)

1 = x ⇒ (1, 2)

2x + y - 12 = 0 and y = 2, hence

2x + 2 - 12 = 0

2x - 10 = 0 (add 10 to both sides)

2x = 10 (divide both sides by 2)

x = 5 ⇒ (5, 2)

y = 2x and 2x + y - 12 = 0 (substitute y = 2x into the second equation)

2x + 2x - 12 = 0

4x - 12 = 0 (add 12 to both sides)

4x = 12 (divide both sides by 4)

x = 3

Substitute x = 3 into y = 2x = (2 * 3) = 6 ⇒ (3, 6)

The coordinates of the 3 vertices are

(1, 2), (5, 2) and (3, 6)